Period cut-off and period-color relation are two special characters of W UMa-type contact binaries. In the past, many authors noted these two properties, however, a comprehensive study was still lacking. In order to reveal a theoretical mechanism behind these two peculiarities, we collected 370 contact binaries whose orbital periods, mass ratios, masses and radii are compiled and attempted to make this idea come true by statistical means. Then, we obtained a lower limit (0.15 days) of orbital period by studying the correlation among four physical parameters (orbital period P, mass ratio q, mass of primary star M1 and separation between two components a). Furthermore, we used the most reliable parameters (P and q) to check our result, fortunately, all evidence indicated that our predicted value is credible. In the end, the reason why the period-color relation exist was also discussed.